For lovers of satire there was a splendid moment last week when the BBC's ambitious redevelopment plans were described as having created "the largest hole in central London". The Broadcasting House redevelopment has been in the spotlight because the National Audit Office, which may have been impressed by the size of the hole, was nonplussed by the size of the budget overrun.

The building is four years late and is £100m costlier than it should be, according to the independent review. Mark Thompson, whose coat of arms should bear a rampant dustpan and brush, has been trying to downsize the ambitions of his predecessor, Greg Dyke. Unfortunately the chickens of the BBC's £2bn infrastructure expansion, which is creating lavish facilities in Scotland and Salford as well as digging a sizeable hole in the West End, are coming home to roost during his period as director general.

The response to the damning report from the NAO was a clever leak to the Murdoch press (who need to be reminded on a daily basis of the value of the BBC) outlining the likely cuts that would be implemented by the corporation's own strategic review. The first two kittens to go into the weighted sack are 6 Music and Asian Network. Both radio services with niche but highly appreciative audiences and very low budgets.

The immediate reaction was an outcry by listeners who objected to having these vital areas of their listening taken away (perhaps). In a possibly historic instance of the BBC's PR operation actually getting something right, the corporation managed to obscure a story about its undoubtedly profligate overspending with one that reminded people why they are happy to pay the licence fee.

Other supposed areas for curtailment include the "cutting in half" of the BBC's website. It is hard to know what it looks like when you cut a website in half, and more bafflingly this is meant to be achieved by a 25% funding cut, which leaves the equation a little hazy – dropping a quarter of the resource but halving the content. Indeed, if one factors in the apparently rising budgets in the future media and technology division, which is separate from the bbc.co.uk budget line, it doesn't really appear that much will be axed at all – more likely changed.

What the episode illustrates is that the BBC is all things to all people, so to mess with its output invites public outrage; and while there is a general demand for a less profligate institution, there is no appetite for closure. The very same people who despise the idea of high-salaried stars would take to the streets to defend the diversity of listening and viewing represented by some BBC services on the at risk register.

From a strategic point of view the BBC is right to be thinking about closing down stations or narrowing output. But perhaps not those plucky services in the niches so far identified (watch out for a third kitten, BBC4, to be added to the sack). With both the iPlayer technology and the upcoming radio player, plus a rapidly digitising archive, it is hard to imagine why the corporation will need its current breadth of packaged output. It will be able to dominate both broadcast and on-demand media for the foreseeable future through the quality of its programmes and the effectiveness of its delivery technology.

In the current landscape, no outcome will please everyone. Logically, though, the organisation is too big, as its income is not reflecting that of the media environment. The hole that the BBC is still in is the issue of its revenue stream. How it apportions costs and what it closes is a matter for the corporation and its vast, multifaceted audience.

There have been a lot of big mistakes at the BBC recently, leading to jitteriness and a lack of confidence. But it remains supremely powerful. Is it moving in the right direction? And what does its future hold?